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© 2011

Classical Summation in Commutative and Noncommutative L<sub>p</sub>-Spaces

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2021)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Andreas Defant
    Pages 1-13
  3. Andreas Defant
    Pages 15-78
  4. Andreas Defant
    Pages 79-158
  5. Back Matter
    Pages 159-173

About this book

Introduction

The aim of this research is to develop a systematic scheme that makes it possible to transform important parts of the by now classical theory of summation of general orthonormal series into a similar theory for series in noncommutative $L_p$-spaces constructed over a noncommutative measure space (a von Neumann algebra of operators acting on a Hilbert space  together with a faithful normal state on this algebra).

Keywords

46-XX; 47-XX Menchoff-Rademacher type theorems noncommutative $L_p$-spaces pointwise convergence of orthonormal series summation methods of orthonormal series symmetric spaces of operators

Authors and affiliations

  1. 1.Department of MathematicsCarl von Ossietzky University OldenburgOldenburgGermany

Bibliographic information

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Reviews

From the reviews:

“The book under review is a beautiful and original exposition on the topic of almost everywhere convergent orthonormal series. … The student or researcher who succeeds in reading this book will be rewarded with a deep understanding of the subject, both in the commutative and noncommutative setting. … the book should stand on the shelf of anyone seriously interested in functional analysis and/or probability.” (Stanisław Goldstein, zbMATH, Vol. 1267, 2013)

“This book is well written, with a concise, clear and readable style. It is divided into 3 chapters and includes a preface, a bibliography consisting of 98 items, and symbol, author and subject indexes. … The book is a good source for specialists and graduate students working in functional analysis and operator theory.” (Mohammad Sal Moslehian, Mathematical Reviews, Issue 2012 d)